@MASTERSTHESIS\{IMM2013-06672,
    author       = "J. L. Pedersen",
    title        = "Bifurcation Analysis of Chemical Reactors with Energy Feedback",
    year         = "2013",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Matematiktorvet, Building 303B, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisor: Morten Br{\o}ns, mobr@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "This thesis is a study of packed-bed reactors with integrated heat exchangers with focus on bifurcation analysis. A mathematical model of a packed-bed reactor is derived using the molar mass- and energy balance equations. This model is discretized using the method of lines in order to make simulations of the steady state of the system. Furthermore disturbances are added to the inlet conditions and it is shown through simulations that this causes moving hot spots as a consequence of the convective instability of the system. An analysis of the parameters’ effect on the steady state is performed together with a bifurcation analysis that shows that no bifurcations occurs in a given parameter space that covers many different processes in the chemical industry.
The theory of a heat exchanger is presented and a model of a such is derived. This model is integrated with the model of the packed-bed reactor in order to perform simulations and bifurcation analysis. Simulations show that disturbances are amplified in the reactor and fed back through the heat exchanger causing growing temperature waves. It turns out that these waves stop growing and end up oscillating with a constant amplitude. This is confirmed by bifurcation analysis that shows the occurrence of both Hopf- and limit point bifurcations. It is shown that bifurcations only occur for changes in the Damk{\"{o}}hler number, the dimensionless adiabatic temperature rise, the flow factor and the dimensionless temperature approach. Finally it is shown that a cooled reactor lowers the amount of bifurcations."
}